A society enters the federation when all its members ask for membership?

In two of the early Star Trek novels, Price of the Phoenix and Fate of the Phoenix, a planet is invited to join the Federation, there was supposed to be a planet wide discussion, followed by a vote whether or not to join. The end result was the entire planet descended into civil war as the populace divided into factions.

all its members ask for membership

You'll never get one hundred percent of a populace to agree to anything, a clear majority probably would suffice. Or the decision might be made by the existing leadership, if the their political system allows them to make that level of decision.

It's possible that the Federation might require a plebiscite as a condition on membership.

Considering the draconian prime directive interpretation of the 24th century, the federation integrating new members (aka interfering) is practically a plot hole:

Interpretation of the PD does seem to change over the course of the multiple series. Possible the PD is concidered part of the Federation government's foreign policy, as various Presidents and foreign secretaries come and go the PD get reinterpreted, rewritten and it various sections assigned different levels of priorities. Every few months Starfleet Captains will receive the latest updates and revisions.